|x+3| horizontally stretch by factor of 4

To apply a horizontal stretch by a factor of 4 to the function \( |x + 3| \), you need to replace \( x \) with \( \frac{x}{4} \) in the expression. This is because a horizontal stretch by a factor of \( k \) is achieved by replacing \( x \) with \( \frac{x}{k} \).

So, the transformed function is:

\[
\left|\frac{x}{4} + 3\right|
\]

This represents a horizontal stretch of the graph \( |x + 3| \) by a factor of 4.

Would you like to see a detailed explanation, or do you have any questions?

Here are some related questions you might find interesting:
1. What is the effect of a horizontal compression by a factor of 2 on \( |x - 2| \)?
2. How would you vertically stretch the function \( |x + 3| \) by a factor of 3?
3. What happens to the function \( |x| \) when it is reflected over the y-axis?
4. How does a horizontal shift of 5 units to the left affect \( |x + 3| \)?
5. What is the effect of a vertical translation of 2 units downward on \( |x + 3| \)?
6. How would you describe a transformation that results in \( \left|\frac{x}{2} - 4\right| \)?
7. How do you horizontally stretch the quadratic function \( x^2 \) by a factor of 3?
8. What is the general formula for a horizontal stretch of a function \( f(x) \) by a factor of \( k \)?

**Tip:** When dealing with transformations, always consider how the function's input (x) or output is being altered to understand the change in the graph.

Learn how to apply a horizontal stretch by a factor of 4 to the function |x + 3|. This transformation involves replacing x with x/4 in the original function. Understand the effect of horizontal stretching on function graphs. Suitable for Grades 10-12 students and anyone interested in function transformations.

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